This is an exam question on a past paper.
"Determine the orbits of the symmetric group $S_{n}$, $n\geq 4$, on the set of pairs of 2-subsets of $\{1,2,\ldots,n\}$"
I'm really not sure what this question means, particularly what the question means by "pairs of 2-subsets of $\{1,2,\ldots,n\}$". Any help clarifying what this means would be amazing.
Pair usually means ordered pair, so a pair of 2-subsets would look something like $(\{a,b\},\{c,d\})$, where $a,b,c,d\in \{1,2,\dots,n\}$. For example, $(\{1,2\},\{2,3\})$. This is the same as $(\{2,1\},\{2,3\})$, since order within a subset does not matter, but different than $(\{2,3\},\{1,2\})$, since order within an ordered pair does matter.